Leftist leader Tsipras was greeted by a mixture of boos and cheers as he addressed the European Parliament on Wednesday, defending his decision to hold a bailout referendum last Sunday that dismayed Europe.
"The Greek government will tomorrow file new concrete proposals, credible reforms, for a fair and viable solution," Tsipras told European lawmakers in Strasbourg, France during a heated debate.
Tsipras also appealed for unity on all sides after six months of deep rifts with eurozone colleagues over the Greek debt crisis, saying: "let us not allow it to become a divided Europe."
Read: Greece 'No' in referendum sends euro into tailspin
But EU President Donald Tusk warned that a special summit of EU leaders on Sunday was the final chance for a deal to avoid a "Grexit", an exit from the single currency that would have global repercussions.
"This is really and truly the final wake-up call for Greece and for us, our last chance," said Tusk, warning that failure "may lead to the bankruptcy of Greece" and cause geopolitical problems for Europe.
Greece's banks remain closed for a second week, amid a cash crisis which saw the country last month become the first developed economy to default on an International Monetary Fund loan payment.
Eurozone leaders lost patience at a crisis meeting in Brussels on Tuesday after Tsipras and his new Finance Minister Euclid Tsakalotos turned up without any concrete plans on paper.
They ordered Athens to file a complete reform plan by midnight (2200 GMT) on Thursday, with Tusk saying the "final deadline" for a deal would then be Sunday's summit of all 28 European Union leaders.
The Greek government promised Wednesday it would start pension and tax reforms next week, as demanded by creditors, in return for a three-year loan to drag its financial system back from the brink of collapse.
In a formal letter to the European Stability Mechanism, the lender of last resort set up during the eurozone debt crisis, Tsakalotos said Greece would "immediately implement a set of measures as early as the beginning of next week".
The ESM confirmed that it had "received the Greek request", the first step demanded by the eurozone leaders towards reaching a deal that many countries remain sceptical about.
Greece has had two previous international bailouts worth 240 billion euros, the last of which expired on June 30.
The price of those loans was five years of harsh austerity measures, and in Sunday's Greek referendum voters overwhelmingly rejected more of the same offered by international creditors.
But the cost of the no vote is also draining Greece dry, with ATM withdrawals limited to just 60 euros per day for Greek bank card holders.
Fears about food supplies in the next two or three weeks have mounted, businesses are unable to pay abroad for goods, and last-minute tourist reservations have plunged 30 percent, the Greek Tourism Confederation said.
The urgency of the situation was underlined by the head of France's central bank, Christian Noyer, who said he feared Greece could descend into "chaos" unless a deal was struck this week.
Noyer told French radio said it was "impossible" to reopen the banks while confidence was so low because there would be an "immediate run" on deposits.
The European Central Bank has been providing emergency liquidity to keep Greek banks from collapsing, but further support will depend on political developments in Brussels and Athens.
A European banking source said that "exasperation and impatience are mounting in the council of governors of the European Central Bank in the face of the attitude of the Greek government".
On Tuesday, European Commission President Jean-Claude Juncker warned "we have a 'Grexit' scenario prepared in detail" if no deal is reached, although he insisted he wanted Athens to stay in the single currency.
German Chancellor Angela Merkel meanwhile insisted that writing off any part of Greece's 320-billion-euro ($350-billion) debt mountain was out of the question.
World stocks saw mixed signals, with Asian and US shares sinking but European stocks edging higher on hopes of a deal. The euro advanced to $1.1041 from a five-week low of $1.0916 in New York trade on Tuesday.
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